Blar i Institutt for matematiske fag på tidsskrift "Journal of Computational Dynamics"

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    • Algebraic structure of aromatic B-series 

      Bogfjellmo, Geir (Journal article; Peer reviewed, 2019)
      Aromatic B-series are a generalization of B-series. Some of the algebraic structures on B-series can be defined analogically for aromatic B-series. This paper derives combinatorial formulas for the composition and substitution ...

    • B-series for SDEs with application to exponential integrators for non-autonomous semi-linear problems 

      Adugna Arara, Alemayehu; Debrabant, Kristian; Kværnø, Anne (Journal article; Peer reviewed, 2024)
      In this paper a set of previous general results for the development of B–series for a broad class of stochastic differential equations has been col- lected. The applicability of these results is demonstrated by the derivation ...

    • B-stability of numerical integrators on Riemannian manifolds 

      Arnold, Martin; Celledoni, Elena; Cokaj, Ergys; Owren, Brynjulf Rustad; Tumiotto, Denise (Peer reviewed; Journal article, 2024)
      We propose a generalization of nonlinear stability of numerical one-step integrators to Riemannian manifolds in the spirit of Butcher's notion of B-stability. Taking inspiration from Simpson-Porco and Bullo, we introduce ...

    • B-stability of numerical integrators on Riemannian manifolds 

      Arnold, Martin; Celledoni, Elena; Cokaj, Ergys; Owren, Brynjulf Rustad; Tumiotto, Denise (Peer reviewed; Journal article, 2024)
      We propose a generalization of nonlinear stability of numerical one-step integrators to Riemannian manifolds in the spirit of Butcher's notion of B-stability. Taking inspiration from Simpson-Porco and Bullo, we introduce ...

    • Deep learning as optimal control problems: models and numerical methods 

      Benning, Martin; Celledoni, Elena; Ehrhardt, Matthias J.; Owren, Brynjulf; Schönlieb, Carola-Bibiane (Journal article; Peer reviewed, 2019)
      We consider recent work of [11] and [6], where deep learning neuralnetworks have been interpreted as discretisations of an optimal control problemsubject to an ordinary differential equation constraint. We review the first ...

    • DETECTING AND DETERMINING PRESERVED MEASURES AND INTEGRALS OF BIRATIONAL MAPS 

      Celledoni, Elena; Evripidou, Charalambos; McLaren, David I.; Owren, Brynjulf; Quispel, G.R.W.; Tapley, Benjamin Kwanen (Peer reviewed; Journal article, 2022)
      In this paper we use the method of discrete Darboux polynomials to calculate preserved measures and integrals of rational maps. The approach is based on the use of cofactors and Darboux polynomials and relies on the use ...

    • On the preservation of second integrals by Runge-Kutta methods 

      Tapley, Benjamin Kwanen (Peer reviewed; Journal article, 2023)

    • REMARKS ON SOLITARY WAVES IN EQUATIONS WITH NONLOCAL CUBIC TERMS 

      Marstrander, Johanna Ulvedal (Journal article; Peer reviewed, 2024)
      In this overview paper, we show existence of smooth solitary-wave solutions to the nonlinear, dispersive evolution equations of the form ∂tu +∂x(Λsu+uΛru2) = 0, where Λs,Λr are Bessel-type Fourier multipliers. The linear ...

    • Symplectic integration of PDEs using Clebsch variables 

      McLachlan, Robert I.; Offen, Christian; Tapley, Benjamin (Journal article, 2019)
      Many PDEs (Burgers' equation, KdV, Camassa-Holm, Euler's fluid equations, …) can be formulated as infinite-dimensional Lie-Poisson systems. These are Hamiltonian systems on manifolds equipped with Poisson brackets. The ...